The tread of a snowmobile ordinarily is supported by a frame which in turn is connected to the snowmobile body by springs and levers in such a manner that the tread-supporting frame may move or "give" somewhat with respect to the body when the snowmobile traverses rough terrain. In general, spring-loaded connected levers are employed to join the frame of a snowmobile to the body, and the relative movement which is permitted between the frame and the body is limited by the distance the connecting levers may travel. For example, in U.S. Pat. No. 3,485,312, movement of the snowmobile frame with respect to the body is limited by the distance that upper ends of the connecting levers can travel between upper and lower longitudinal members of the frame. Similarly, in U.S. Pat. No. 3,613,811, the movement of the frame upwardly towards the body is limited by the distance which the connecting levers may travel. A reliable suspension system which would permit greater relative movement between the frame and the body is much to be desired.